tooth for a coin as they sleep. The child who does so and routinely finds a coin the next morning, has an empirically warranted belief in the semantics describing a winged person that leaves coins under pillows and is called a “tooth fairy”. This belief is no less empirical than belief in the semantics positing an invisible force that pulls apples from their trees to the ground and is called “gravity”. But should the child forget to advise his mother that he placed a recently lost tooth under his pillow, he will rise the next morning to find no coin, and may become suspicious.
Then like the bird watcher with a red raven-looking bird, the child has semantical and ontological choices. He may continue to define “tooth fairy” as a benefactor other than his mother, and reject the tooth-fairy semantics and ontology as inadequately realistic. Or like the astronomers who concluded that the morning star and the evening star are the same luminary and not stellar, he may revise his semantics of “tooth fairy” to conclude that his mother and the tooth fairy are the same benefactor and not winged. But later when he publicly calls his mother “tooth fairy”, he will be encouraged to revise this semantics of “tooth fairy”, and to accept the more conventional ontology that excludes tooth fairies, as modern physicians exclude demons. This sociology of knowledge and ontology has been insightfully examined by the sociologists of knowledge Peter Berger and Thomas Luckmann in their Social Construction of Reality.
Or consider ontological relativity in fictional literature. “Fictional ontology” is an oxymoron. But fictional literature resembles metaphor, because its discourse is recognized as having both true and false aspects (Section 3.27). For fictional literature the reader views as true the parts of the text that reveal reality adequately, and the reader views as untrue the parts that are fictional. Sympathetic readers, who believe Mark Twain’s portrayal of the slavery ontology, recognize an ontology that is realistic about the racist antebellum South. And initially unsympathetic readers who upon reading Twain’s portrayal of Huckleberry Finn’s dawning awareness of fugitive slave Jim’s humanity notwithstanding Huck’s racist upbringing, may thus be led to accept the more realistic ontology that is without the dehumanizing fallacies of the South’s racism. Ontological relativity enables recognition that such reconceptualization can reveal a more realistic ontology not only in science but also in all discourse including even fiction.
Getting back to science, consider the Eddington eclipse test of Einstein’s relativity theory mentioned above in the discussion of componential semantics (Section 3.22). That famous astronomical test is often said to have “falsified” Newton’s theory. Yet today the engineers of the U.S. National Aeronautics and Space Administration (NASA) routinely use Newton’s physics to navigate interplanetary rocket flights through our solar system. Thus it must be said that Newton’s “falsified” physics is not completely false or NASA could never use it. The Newtonian ontology is realistic, but is now known to be less realistic than the Einsteinian ontology, because the former has been demonstrated to be less empirically adequate.
There is no semantically interpreted syntax that does not reveal some more or less realistic ontology; since all semantics is relativized and ultimately comes from sense stimuli, no semantically interpreted syntax is utterly devoid of ontological significance.
3.39 Causality
Cause and effect are ontological categories, which in science can be described by tested and nonfalsified nontruth-functional hypothetical-conditional statements thus having the status of laws. The nontruth-functional hypothetical-conditional statement claiming a causal dependency is an empirical universal statement. It is therefore never proved and is always vulnerable to future falsification. But ontological relativity means that a statement’s empirical adequacy warrants belief in its ontological claim of causality, even if the relation is stochastic. Nonfalsification does not make the statement affirm merely a Humean constant conjunction. When in the progress of science a causal claim is empirically falsified by empirical testing, it is made evident thereby that the causality claim is less adequately true and thus less realistic than previously hypothesized.
3.40 Ontology of Mathematical Language
In the categorical proposition the logically quantified subject term references individuals and describes the attributes that enable identifying the referenced individuals, while the predicate term describes only attributes without referencing the instantiated individuals manifesting the attributes. The referenced extramental real entities and their semantically signified extramental real attributes constitute the ontology described by the categorical proposition that is believed to be true due to its experimentally or otherwise experientially demonstrated empirical adequacy. These existential conditions are expressed explicitly by the copula term “is” as in “Every raven is black”.
However, the ontological claim made by the mathematical equation in science is not only about instantiated individuals or their attributes. The individual instances referenced by the descriptive variables in the applied mathematical equation are instances of individual measurement results, which are acquired by executing measurement procedures that yield numeric values for the descriptive variables. The individual measurement results are related to the measured reality by nonmathematical language, which includes description of the measured subject, the metric, the measurement procedures, and any apparatus described in test-design language. Also calculated and predicted values for descriptive variables describing effects in equations with measurement values for other variables describing causal factors make ontological claims, which are tested empirically. Untested theories make relatively more hypothetical quantitative causal claims. Tested and nonfalsified equations make quantitative causal laws.
D. PRAGMATICS
3.41 Pragmatic Dimension
Pragmatics is the functions of language.
Linguists recognize the pragmatics of ordinary English when they distinguish the four moods, namely the declarative, interrogative, imperative and exclamatory moods. The intended mood can be indicated syntactically by word order and/or punctuation marks, and phonetically by voice inflection. The moods can be exemplified in the language of science, but philosophers of science make pragmatic distinctions that are more specifically functional for basic research in empirical science:
The pragmatics of basic research in science is theory construction and empirical testing, in order to produce laws for explanations.
Pragmatics is the metalinguistic dimension after syntax, semantics and ontology, and it presupposes all of them. The regulating pragmatics of basic science is set forth in the statement of the aim of science, namely to create explanations containing scientific laws by development and empirical testing of theories, which are deemed laws when not falsified by the currently most critically empirical test. Explanations and laws are accomplished science, while theories and testing are work in progress at the frontier of basic research. Understanding the pragmatics of science requires understanding theory development and testing.
3.42 Semantic Definitions of Theory Language
For the extinct neopositivist philosophers the term “theory” refers to universally quantified sentences containing “theoretical terms” that describe unobserved phenomena or entities. The nineteenth-century positivists such as the physicist Ernst Mach rejected theory, especially the atomic theory of matter in physics, because atoms had never been observed. These early positivist philosophers’ idea of discovery consisted of induction, which yields empirical generalizations rather than theories that contain theoretical terms.
Later the twentieth-century neopositivists believed that they could validate the meaningfulness of theoretical terms referencing unobserved microphysical particles such as electrons, and thus admit theories as valid science. But for discovery of theories
